Extending the formalism in order to enlarge the set of improper gauge transformations may not be always direct or possible, as the papers [1]}, [2]} have shown for the minimal electromagnetic coupling. What makes the extension work in the case of supergravity is the fact that the abelian part of the supersymmetry transformation dominates the non abelian corrections, as for pure gravity [3]}, while this is not so for Yang-Mills theory where the derivative operator \(\partial _k\)  and the connection \(A_k\)  are of same order \(\mathcal {O}(r^{-1})\) . The difficulty is somewhat reminiscent of the “boost problem” in field theories [4]} and also of the difficulties encountered in imposing asymptotically the Lorenz gauge in the case of electrodynamics with massless charged fields [2]}, [6]}.
